@dharr Hi dear Dr.David
i am glad to have your response again, in fact i want  in (G1) we have some function term and other are parameter like 1/G(xi)*($$$$$$$$$$$$+diff(G(xi),xi)(##########) we have something like that i want collect 1/G(xi)*diff(G(xi),xi)/G(xi) then finding term i must do this by hande if there is no any code for get the solution of our ODE, i did collect almost but how i can arrange them by code automaticaly not use any hande, this code in eqs are used is useful for some function with one term i wanna know is work for this kind of function too or not?

@janhardo  thanks i will do another post soon i am work in simple equation  in laplace i will try do this stuff of adomian by integral is old way but it is work for me , also have a lot step  try your best if finish upload mw

@janhardo  i have other info too just ask what you need?
also there is another easy method if you can't do this i will ask anotehr question about taking adomian polynomial by intgral is easy for writing program i don't know writing program otherwise i will do i know each step by hand  but for programing i am not able to write now , but i will learn one day

@janhardo can you do for multiply or how you gonna make a prc just i change a function with subscript and the procedure work becuase thus example i want to solve are so complicate
can you construct the exact shape algorith becuase this ethod in top picture are so easy if you can write that it will be emazing

@janhardo please do by yourself i don't know where i put it in and upload file , i will distroy

@nm you did a great job, i wish i know your coding... beliave me when i watched your code i didn't know where you calculate relative error i didn't find it except division but didn't have a name....
i want add two other term if possible  each one alone like exact solution in one column aprroximate in one column and error in one column also relative error your code is high level i can't involve but i liked so much.
can you answer my other question it seems you can hundle them too ? i am waiting for each one of them

@janhardo  the zhao method is easy is so  easy with your coding you can write easily

@Alfred_F I like your information specially your link
if have any link about soliton solution give me the link

@janhardo this adomian but not in shape of top algorithm, how we apply this for the second example I have problem with this kind example  I  have problems with two one more variable , and make your outcome more prettier and be better if instead of results outcome be like this A[0]=@ next line A[1]=# so on 

@janhardo they delete a lot i have other question too but no one answer this, i think is easy for them becuase even program is write in front of them but why they don't envolve, i have other post question but i need this adomian polynomial i have  other  coding but is not usfull for all function , i think this will be answer for all of kind function but how do by procedure and make a good design for it , i think this question will remain  becuase is hard to write program 

@Alfred_F in type two dont have direvitive i think i solve the first one two but step is two much i need someone to reduce my step in procedure i take to much time like that i need speed 

@acer  why didn't tell me before that u am new where i should know this i will post 1000 question like that without deleting i didn't post a questions becuase of that i  have a lot question but there is no one can answer this is problem
thank you sir and sorry if i disrespect in any kind 

@Alfred_F  the painleve  have first derivative with degree two i think is different , also this one must have a technique , maple must have a way to solve this kind of approximating solution easily more than other program i have to find best way calculating ODE and PDE by this LDM

@one man  the reason is that they say the question is same to the last question, they right is same topic but not same question they say i must add to that question and add to that question i posted a weak before like that no one see new update in question, today they delete more then 4 post of mine all of them are different, different algorithm and i spend time to post thus and waiting for answer otherwise if i know thus answer why i should ask in here .

@janhardo moderator did
is not just two he did atmost 10 of my questions i will upload the algorithm really i am need that